# If a sample originally had 120 atoms of carbon-14, how many atoms will remain after 16,110 years?

##### 1 Answer

We know that carbon-14 (

So, **zero-order** process that follows a half-life decay mechanism.

The **half-life** with respect to the **rate constant** would be found to be:

#t_"1/2" = (ln2)/(k)# where the point of showing the equation is that it does

notdepend on the concentration of#""^14 "C"# , which is what a zero-order process is.

Logically, what happens in a **half**-life decay is that **half** the sample becomes something else, so of course, when we focus on the original sample, we would see that **half** is left when the process has occurred **once**.

After each **half**-life passes by, we lose **half** of the remaining sample, so you can see that we can simply **halve** the concentration **half**-lives.

It therefore makes sense that after

#color(blue)([""^14 "C"]_f = 1/(2^n)[""^14 "C"]_i)#

Using the half-life of carbon-14, which is known to be about

#= 1/(2^("16110/5730"))[""^14 "C"]_i#

We would actually see that this gives the final concentration of